In summarising what can be drawn from scripture about these institutions, Ira M. Price (a founding faculty member of the University of Chicago, professor of ancient languages and literatures) concluded1:

...The sons of the prophets 1) were collected together in bands or schools; 2) in six different localities, viz., (a) Ramah, (b) Bethel, (c) Gilgal, (d) Jericho, (e) Carmel, (f) Samaria; 3) Under the tuition of (a) Samuel, (b) Elijah, (c) Elisha; 4) with instruction in (a) prophesying-worship, (b) sacred music, (c) practical matters of their day; 5) with their time wholly occupied in (a) study and worship, (b) doing errands for their masters and God, (c) performing the regular duties of a prophet; 6) largely dependent for their support on the charity of the people.

2. Training mandate given to the New Testament Office of Prophet

In instructing the Ephesian church with regard to spiritual gifts, the Apostle Paul had the following to say:

7 But to each one of us grace was given according to the measure of Christ’s gift. 8 Therefore He says:

“When He ascended on high,
He led captivity captive,
And gave gifts to men.”

9 (Now this, “He ascended”—what does it mean but that He also first descended into the lower parts of the earth? 10 He who descended is also the One who ascended far above all the heavens, that He might fill all things.)

11 And He Himself gave some to be apostles, some prophets, some evangelists, and some pastors and teachers, 12 for the equipping of the saints for the work of ministry, for the edifying of the body of Christ, 13 till we all come to the unity of the faith and of the knowledge of the Son of God, to a perfect man, to the measure of the stature of the fullness of Christ; 14 that we should no longer be children, tossed to and fro and carried about with every wind of doctrine, by the trickery of men, in the cunning craftiness of deceitful plotting, 15 but, speaking the truth in love, may grow up in all things into Him who is the head—Christ— 16 from whom the whole body, joined and knit together by what every joint supplies, according to the effective working by which every part does its share, causes growth of the body for the edifying of itself in love. - Ephesians 4:7-16 NKJV

Those who advocate for modern day schools of prophecy generally interpret this passage as:

The role of the office gifted is not so much to do the work of ministry themselves, but primarily to train the saints to do the work of ministry (v12).

The type of training offered by five-fold ministers varies according to their gifts - Apostles excel in training the Church to be more apostolic, Prophets excel in trainging the Church to be more prophetic etc.

THE MINISTRIES OF CHRIST - We believe in the full function of the five-fold ministry which was given to perfect and equip the saints so they can enter into the work of their ministry, thereby edifying the whole Body of Christ. [Eph. 4:11-16; I Cor. 12:28.] We believe in the present day ministries of the apostles and prophets, which Christ has set in the Church as foundational and revelational ministries. We believe these two ministries will be restored to function in full power and authority before the literal second coming of Christ. [Eph. 2:20; Acts 3:21.]

The associated ecclesiology is explained a little more under:

ORDINANCES - We believe in two primary New Testament ordinances: Baptism by immersion and The Lord's Supper. However, we do not believe that the administration of such ordinances is limited to ordained or licensed ministers. We believe in the priesthood of believers. Ordination and licensing in this organization is a separation and recognition of a specific gifting of God. We believe that God calls men into specific ministries as apostles, prophets, evangelists, pastors, and teachers. God calls. Man can only recognize the call and acknowledge it. Ordination is on the basis of that recognition of God's gifting. Men called to a specific office by God and ordained or licensed by this organization will have the right to participate in the traditional sacramental and ordinal functions of the organization such as marriage, funerals, baptisms, and the like. They shall also be expected to function in the spiritual gifting(s) of their office and to demonstrate the reality of their calling. This organization is a non-sacramental protestant group. We reject the efficacy of ritual and the concept of a separate priestly class. We recognize the priesthood of believers and the serving ministry of the apostle, prophet, evangelist, pastor, and teacher with government by elders. As such, we recognize that those called to those offices will function in a manner to lead by example in prayer, worship, teaching, laying on of hands, and prophesying and that such action on the part of those ordained and licensed by this organization are equivalent to the sacramental function of the priesthood in traditional sacramental churches.

Does this question consider the comment Moses made on a certain occasion:

... would that they were all prophets.

(Numbers 11: 24-29)

24 And Moses went out, and told the people the words of the Lord, and
gathered the seventy men of the elders of the people, and set them
round about the tabernacle.

25 And the Lord came down in a cloud, and spake unto him, and took of
the spirit that was upon him, and gave it unto the seventy elders: and
it came to pass, that, when the spirit rested upon them, they
prophesied, and did not cease.

26 But there remained two of the men in the camp, the name of the one
was Eldad, and the name of the other Medad: and the spirit rested upon
them; and they were of them that were written, but went not out unto
the tabernacle: and they prophesied in the camp.

27 And there ran a young man, and told Moses, and said, Eldad and
Medad do prophesy in the camp.

28 And Joshua the son of Nun, the servant of Moses, one of his young
men, answered and said, My lord Moses, forbid them.

29 And Moses said unto him, Enviest thou for my sake? would God that
all the Lord’s people were prophets, and that the Lord would put his
spirit upon them!

And also Exodus 19: 6:

And ye shall be unto me a kingdom of priests, and an holy nation.
These are the words which thou shalt speak unto the children of
Israel.

And this is echoed in 1 Corinthians 14: 5:

I would that ye all spake with tongues, but rather that ye
prophesied: for greater is he that prophesieth than he that speaketh
with tongues, except he interpret, that the church may receive
edifying.

It seems to me that the entire chapter 14 is basically instructing the believers in how to use their gifts of prophecy, and how to teach each other.